具有广义Virasoro对称代数的(3+1)维Painlevé可积模型

VIRASORO INTEGRABLE AND PAINLEV? INTEGRABLE MODELS IN (3+1)-DIMENSIONS

寻找高维可积模型 (特别是 3 + 1维可积模型 )是非线性物理中的一个非常重要的问题 .建立了一种利用广义Virasoro对称性的高维实现首先找到了一些 (3 + 1)维Virasoro可积模型 ,并证明 (3+ 1)维Virasoro可积模型均具有Kac Moody Virasoro对称代数 .更进一步 ,利用Weiss Tabor Carnevale的奇性分析方法 ,证明了其中一个Virasoro可积模型也是Painlev啨可积的 .

Seeking higher\|dimensional integrable models is very important in nonlinear science. In this paper, using the generalized Virasoro type algebra, many (3+1)\|dimensional Virasoro models are integrable under the meaning that they possess infinitely many symmetries. All of the (3+1)\|dimensional models are proved to have Kac\|Moody\|Virasoro symmetry algebra. In addition, using WTC Painlevé analytical approach, a (3+1)\|dimensional Virasoro model is integrable under the meaning that it possesses the Painlevé property.